ARTICLE IN PRESS
Quaternary Geochronology xxx (2010) 1e7
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Research Paper Methods and code for ‘classical’ age-modelling of radiocarbon sequences
Article history: Ageedepth models form the backbone of most palaeoenvironmental studies. However, procedures for Received 19 February 2009 constructing chronologies vary between studies, they are usually not explained sufﬁciently, and some are Received in revised form inadequate for handling calibrated radiocarbon dates. An alternative method based on importance 22 October 2009 sampling through calibrated dates is proposed. Dedicated R code is presented which works with calibrated Accepted 27 January 2010 radiocarbon as well as other dates, and provides a simple, systematic, transparent, documented and Available online xxx customizable alternative. The code automatically produces ageedepth models, enabling exploration of the impacts of different assumptions (e.g., model type, hiatuses, age offsets, outliers, and extrapolation). Keywords: Ó Radiocarbon age-modelling 2010 Elsevier B.V. All rights reserved. Calibration Software Exploratory analysis
1. Introduction “classical” ageedepth modelling such as linear interpolation (31) or linear/polynomial regression (18). Ageedepth models are built to estimate the calendar ages of As will be discussed below, calibrated 14C dates often have irreg- depths in a core from a deposit, based on limited numbers of dated ular distributions which cannot be properly reduced to single point depths and on assumptions as to how the deposit has accumulated estimates with symmetric error bars. However, most age-modelling between those dated depths. Given the intensive use of ageedepth routines do indeed simplify calibrated distributions to symmetric modelling, surprisingly few details have been published about the ones. Bennett (1994) and Bennett and Fuller (2002) discussed basic techniques involved, adequate software seems to be largely missing ageedepth models based on linear interpolation, polynomial and or under-used, and details of applied ageedepth modelling spline regression, but based on uncalibrated radiocarbon dates. Proxy assumptions are often missing in the literature. graphing software Tilia (Grimm, 1990)producesageedepth models, A review of all papers published in 2008 in the journals Quater- but i) does not calibrate dates, ii) does not take into account errors, nary Geochronology, Quaternary Science Reviews, Journal of and iii)doesnotprovideageedepth graphs. Heegaard et al. (2005) Quaternary Science and The Holocene, indicates 93 papers applying applied mixed-effects modelling, but assumed that calibrated 14C some kind of ageedepth model through fossil proxy deposits ages can be approximated by a simpler statistical distribution (e.g., (Table 1). Of these papers, all 82 that used 14C dates provide details Gaussian). It is likely that studies which do not report their about their calibration procedures (e.g., which calibration curve and ageedepth modelling software often use regression or spline func- software were applied). However, often much less information is tions which generally cannot deal with irregular distributions. supplied about subsequent ageedepth modelling (regularly this Whereas proxy graphic software psimpoll (Bennett,1994) can handle information can only be gleaned from graphs). Sixty papers do not tell calibrated 14C dates, they need to be calibrated outside the software. which (if any) point estimates were used, 71 do not mention the Although Bayesian methods can produce very reliable ageedepth software used to produce ageedepth curves, 65 do not indicate models (e.g., Blaauw and Christen, 2005; Bronk Ramsey, 2008), whether ageedepth uncertainties were calculated, and 18 do not Table 1 shows that by far most studies continue to use more basic, specify the applied ageedepth model. Eleven papers apply some ‘classical’ age-depth models (especially for sites with only a handful form of Bayesian ageedepth modelling, whereas the remainder use of dates). Here these classical approaches will be discussed, and a technique based on probability sampling methods will be proposed in order to take into account the multi-modal and asymmetric nature of calibrated 14C dates. A more systematic and transparent approach e * Tel.: þ44 28 9097 3895. to produce classical age depth models is presented, based on free E-mail address: [email protected] and open-source software.
1871-1014/$ e see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.quageo.2010.01.002
Please cite this article in press as: Blaauw, M., Methods and code for ‘classical’ age-modelling of radiocarbon sequences, Quaternary Geochronology (2010), doi:10.1016/j.quageo.2010.01.002 ARTICLE IN PRESS
2 M. Blaauw / Quaternary Geochronology xxx (2010) 1e7
Table 1 Literature analysis of primary literature reporting ageedepth models, published in 2008 in Quaternary Geochronology (2 papers), Quaternary Science Reviews (40), Quaternary Research (10), Journal of Quaternary Science (13) and The Holocene (28). Publications citing previously published ageedepth models were not taken into account. As several papers applied a number of ageedepth models and types of dates, the numbers do not always add up. 17 papers mentioned the removal of dates identiﬁed as outlying.
Dates Point estimate Model Model error Age-model software 14C (82) Not speciﬁed (60) Linear interpolation (31) Not speciﬁed (65) Not speciﬁed (71) Tephra (11) Full distribution (13) Not speciﬁed (18) 2 sd error (17) Oxcal (6) 210Pb/Cs (9) Mid (5) Linear regression (13) 1 sd error (6) Bpeat (4) U/Th (8) Median (4) Bayesian (11) Mixed-effect (3) OSL (5) Intercept (3) Linear regression (5) Bchron (1) Tuning (4) Mean (1) Spline (4) psimpoll þ BCal (1) Varves (2) Weighted mean (1) Mixed-effect (3) Other (2) Mid of most probable range (1) CRS (2) Other (2)